Quantification of Mismatch Error in Randomly Switching Linear State-Space Models

Abstract

Switching Kalman Filters (SKF) are well known for solving switching linear dynamic system (SLDS), i.e., piecewise linear estimation problems. Practical SKFs are heuristic, approximate filters and require more computational resources than a single-mode Kalman filter (KF). On the other hand, applying a single-mode mismatched KF to an SLDS results in erroneous estimation. This paper quantifies the average error an SKF can eliminate compared to a mismatched, single-mode KF before collecting measurements. Derivations of the first and second moments of the estimators' errors are provided and compared. One can use these derivations to quantify the average performance of filters beforehand and decide which filter to run in operation to have the best performance in terms of estimation error and computation complexity. We further provide simulation results that verify our mathematical derivations.

Efficient Model Selection in Switching Linear Dynamic Systems by Graph Clustering

“…This section reviews the calculation of the dissimilarity measures based on [28]. Let l n and q n refer to a sequence of modes representing the ground truth and detected trajectories, respectively, where…”